If we are going with the fact that the dog ate cat feces then you may be looking at a blockage of the intestines. This would show symptoms of vomiting, diarrhea, lethargy, and sudden lack of appetite. A blockage would require surgery so if the other signs start to show along with the drooling and diarrhea then I would have him looked at.

Drooling can be a sign of nausea, a tooth or gum problem, obstruction, ulcers in the mouth , something stuck between the teeth ,or something toxic that the dog has eaten.

I would take the dogs temperature and make sure that is normal. Using a rectal thermometer (found in any drug or grocery store) put Vaseline on the end and insert about one inch into the rectum, hold for two minutes or until it beeps if it is digital. Normal for dogs is 100.5 to 102.5. something higher could indicate infection.

Worms and protazoa can be another reason for the diarrhea and the drooling may be coincidental with something also going on in the mouth. If the car feces was infected with either parasites or protazoa then the dog would have picked it up through ingesting the feces.

If this is just upset stomach you can try giving some pepto bismol, and tonight give a bland diet of boiled chicken and white rice. This will help the intestines to become less inflamed. Here is information on pepto bismol and dosage;